Although our results provide some cautious optimism for distinguishing EQG from GR by observation, tables REF  and REF 
indicate that using Sgr A* to distinguish EQG from corresponding predictions in ECG [1]} will be very challenging. In Figs. REF  and  REF  we compared deviation of the primary image angular position and differential time delay in EQG from ECG for Sgr A*. The deviation of EQG results for angular positions of primary images relative to that in ECG is larger for sources that are further away from the lens, but quite small for \(\beta \approx 1\) . Furthermore, the deviation of EQG results for the differential time delay \(t_d=\tau _s-\tau _p\)  relative to those in ECG is larger for the sources further away from lens and increase with increasing \(\beta \) . The results for the relativistic images in Tables REF  and REF  show that EQG results are small but they have noticeable differences with ECG results [1]}. The situation is not much better for black holes in other galaxies; table REF 
indicates that EQG predictions are quite similar to those in ECG [1]} for the largest possible values of their respective coupling constants. In fact for other galaxies like Sgr A*, EQG and ECG results are quite similar for the special choice \({\cal D}=0.5\)  and \(\beta \approx 1\)  (see Fig. REF ).
While we might hope to distinguish (or place bounds on) non-linear curvature effects of GQTGs using gravitational lensing, it will be very challenging to distinguish between the two simplest GQTGs. One possibility is to incorporate rotation. Slowly-rotating solutions have been obtained
numerically in ECG [4]}, allowing for a computation of the photon sphere and the innermost stable circular orbit. It is reasonable to expect that there will be distinct features that not only distinguish the ECG predictions from EQG, but also distinguish the different EQG theories from each other.
